in a serious 1v1 battle which titan would actually be the strongest?
I promised myself to start doing this btw so major spoiler warning for the manga here!
My first thought is of course the founding titan. It can controll all eldians and you have to be eldian to be a titan shifter so none of the other titans would really be able to fight it at all. Without it's powers the founding titan would probably come in last though because it doesn't have any physical specialties and we saw Frieda with her founding titan loose against Grisha who had no training with teh attack tiatn at all. That could be because of the vow of peacae but in a fight of the founding titan without the ability to control eldians vs any other titan shifter it would probably still loose in most cases.
I'm going to take out the founding titan for this reason. So here is my actual list of what I think would be the strongest shifter.
For the sake of argument i'm giving every shifter the ability to crystallize their body here.
The cart doesn't really have any specialties apart from it's speed and the fact that it walks on four legs. It seems to mainly be used as a means of transportation, for humans, ware and mounted canona. The titan alone probably couldn't win a 1v1 against any of the others here. Pieck made the most of the cart during the final battle and everything she did was creative and very impressive but still the cart is pretty bad for just solo combat.
The armored titan is of course a very strong one but it's still not very usefull most of the time. It has not won a single hand to hand titan fight in the entire story, is very slow and it's enemy found a way to break through it's armor in every fight. It get's faster when it sheds it's armor but at that point it becaomes even more useless because it's ennemies are probably stronger than it and have a better go at attacking it. If it's opponent has the ability to harden parts of it's body the armored tiatn has a 90% chance of losing becase titan hardening seems to be harder than the armored titans armor. That also kidna makes the armored titan obsolete because the other humanoid shaped titans could just use titan hardeing as an armor and do better than the armored. It is only really usefull as a giat shield against non titan attacks or as a wreaking ball to tear down structures but in titan combat it's absolutey garbage.
The beast titan was descirbed as "weak" and "useless in battle" by Tom Xaver. Zeke's beast titan seemed to be an exception to that in that him and his boulders where really useful but he'd probably still suck in 1v1 titan combat. We saw that he beat Reiner but I honestly have no explaination to how he would have done that apart from maybe standing on the walls and just attacking ranged. But as said before if the armored titans oponent has hardening the armored titan has no chance and since Zeke's beast obviously had hardening and every otehr beast titan probably could have had it too I'll just say it's stronger than the armored. The beast titan, isn't made for hand to hand combat. Even Zeke's isn't, he is of course in the advantag in a fight against humans or ships or whatever else he can fight from afar but without a few hundred meter etween him and his enemy and a bunch of coulders to throw he can probably only hold hismelf against the armored titan (and it's surprisingly weak armor). If it wasn't for Zeke's special beast titan and also it's crystalizing abilities I'd probably switch the armored and beast titan though.
The female titan is a pretty versitile one and also relatively ok when it comes to abilties and physicque. With taht I mean it has no real abilities that are useful in battle but it also has no physical features that could be hindering in battle. The crystalizing ability is not one unique to the female titan but for the sake of argument let's give it to her here. The female would probably have a real chance against at least a few of the titans, especially with a skilled user like Annie. She's very flexible and seems to have high endurance as well as a completely humanoid body which is great for titan hand to hand combat. She even would have won against (an admitedly unexpierienced) Eren in Stohess but chose to flee instead of fight. She probably wouldn't stand in a fight against a fully trained attack titan but she did really good and would probably do so against others too.
The attack titan doesn't really have a special battle ability. It just seems to be a bit stronger than the other titans and is with it's 15m among the upper middle of the shifters heights. It's strength relies mostly on Eren's agression and anger, his training and the aquired titan hardening. With the hardening it is definitely also among the stronger of the titans but it is just kinda ordinary apart from that. It's good but not super good. It could hold itself against the female in stohess but lost and they only got Annie because she tried to flee, it won against the armored titan with just some martial arts and luck and in the second and third fight with hardening, it would probably have an easy time winning against the beast in close combat beause the beast (apart from it's arms) seems to be fairly slow. It probably would have a chance against the jaw titan if the terrain was in it's favor but in most cases the jaw would be surperior.
The jaw is small but very versatile and fast. Depending on the rterain it could probably be among the strongest titans. Even if the terain would be a flat field it could still have a massive advantage over it's ennemy. It's relatively small and hard to hit and very fast, that combined with it's jaws and claws could let it do massive damage to it's oponent even if it is phyiscally weaker than the otehr titans. in a terraine like a city or a forest it is even stronger beause it can use the structures to jump around and attack from above giving it an easier time reaching it's oponents neck. It's also able to bite through titan crystalisation which would render all titans that rely on that practically useless.
The colossal titan could obviously just step on all the other titans but even if you ignore that they just wouldn't have a way to kill it. The Jaw could probably climb it but even in that case the collosal could just use it's steam to get rid of it if the sheer heat of the colossal's skin wouldn't have already done that.
The war hammer is in my opinion the strongest of all titan shifters. There are really no downsides to it except the fact that it's shifter isn't in it's neck but it has enough of a defense to excuse that. It is probably the only shifter that has a reasonable chance agains tall others. Even against the colossal (which it could probaby imobilize with it's structures and then attack it's neck with them) as well and the jaw (which it could just entrap or impale with it's structures) it has a reasonable chance. It Would have won againt the attack in Liberio if it hadn't been for the survey corps reenforcement and the various war hammers really impaired the alliance during the finaly battle.